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Function f(x) from the graph f'(x)
- The function is increasing from (-2,0)U(0,2) because between these intervals you get positive outputs. The function is decreasing from (-∞,-2)U(2,∞) because all the outputs in these intervals give you a negative output.
- I think there are three extrema because at three points the slope is equal to zero. At f'(o) the slope is equal to zero which means it is a critical point. Two other points where the slope is equal to zero is at f'(-2) and at f'(2) which makes them two other critical points.
- The function is concave up at about (-∞,-1.2)U(0,1.2) because between theses intervals f''(x) is greater than zero. The function is concave down at (-1.75,0)U(∞,1.75) because f''(x) is less than zero.
- The power function could be -x^5 becuase the f'(x) is negative so i'm guessing would be negative as well. And f'(x) curves four times so the power funtion would be one more up.
1. Excellent!
ReplyDelete2. You found all the critical points well, but you can tell more than that. If the f'(x) CHANGES SIGNS at those points from neg to pos, you have a minimum, like at x=-2. If f' changes from pos to neg, like at x=2, you have a max. If it doesnt change, you have nothing, like at x=0.
3. Great! Now how can you tell that f''>0 from this graph of f'?
4. yup!